数值天气预报模式中的确定性混沌动力学
The Dynamics of Deterministic Chaos in Numerical Weather Prediction Models
摘要：
大气天气系统是相干结构，由离散的云胞组成，形成行/街道、中尺度集群和螺旋带的模式，在行星大气边界层的湍流剪切流中，这些云胞在其可观的生命周期内保持其特性。在过去20年的湍流研究中，湍流中存在拟序结构（似乎是系统运动）已得到充分证实。基于固有的非线性纳维-斯托克斯方程的数值天气预报模式并不能提供实际的预报，因为有以下固有的局限性：（1）大气流动的非线性控制方程没有精确的解析解，对初始条件的敏感性导致了具有确定性混沌特征的混沌解。（2）控制方程没有考虑动力学相互作用和协同作用。湍流波动的完整谱的存在，形成了大的相干天气系统的一个组成部分（3）可用计算机容量的限制使得必须对控制方程进行严格的截断，从而产生近似误差（4）与计算机精度相关的截断误差将前面提到的不确定性随时间呈指数地放大，并且模式预测变得不切实际。因此，准确模拟天气现象需要替代概念和计算技术。本文提出了一种适用于大气边界层相干天气结构形成的确定性混沌普适理论。
英文摘要：
Atmospheric weather systems are coherent structures consisting of discrete cloud cells forming patterns of rows/streets, mesoscale clusters and spiral bands which maintain their identity for the duration of their appreciable life times in the turbulent shear flow of the planetary Atmospheric Boundary Layer. The existence of coherent structures (seemingly systematic motion) in turbulent flows has been well established during the last 20 years of research in turbulence. Numerical weather prediction models based on the inherently non-linear Navier-Stokes equations do not give realistic forecasts because of the following inherent limitations: (1) the non-linear governing equations for atmospheric flows do not have exact analytic solutions and being sensitive to initial conditions give chaotic solutions characteristic of deterministic chaos (2) the governing equations do not incorporate the dynamical interactions and co-existence of the complete spectrum of turbulent fluctuations which form an integral part of the large coherent weather systems (3) limitations of available computer capacity necessitates severe truncation of the governing equations, thereby generating errors of approximations (4) the computer precision related roundoff errors magnify the earlier mentioned uncertainties exponentially with time and the model predictions become unrealistic. The accurate modelling of weather phenomena therefore requires alternative concepts and computational techniques. In this paper a universal theory of deterministic chaos applicable to the formation of coherent weather structures in the ABL is presented.
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